The Lagrange equations for systems with mass varying explicitly with position: some applications to offshore engineering

Pesce, Celso Pupo; Tannuri, Eduardo A.; Casetta, Leonardo

doi:10.1590/s1678-58782006000400015

Cited by 19 publications

(27 citation statements)

References 5 publications

(6 reference statements)

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“…Varying the barge draft the resonant frequencies are larger when a small barge draft is considered. The range of the approximated piston mode frequencies (evaluated by Bunnik et al (2009), Pesce et al (2006 and Molin (2001) formulations) as well as the longitudinal sloshing mode (Molin (2001)) are is in fair agreement with the resonant frequencies found in the motion and wave elevation RAOs.…”

Section: Discussionsupporting

confidence: 73%

“…The same expression has been derived in Pesce et al (2006), for the piston-like mode in a moonpool case. Since the geosim and the barge present different drafts, we consider a range of frequencies defined in terms of both drafts, in which we expect that the piston mode frequency is within inside.…”

Section: Gap Resonant Effectsmentioning

confidence: 68%

“…The physical phenomenon is 95 typical of the moonpool system. The classic piston-mode dynamics in moonpools is nonlinear; see for instance Pesce et al (2006) in absence of platform motion. For small oscillation the linearized equation gives ω = g/T as the piston mode natural frequency, where T is the draft.…”

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confidence: 99%

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Analysis of wave resonant effects in-between offshore vessels arranged side-by-side

Dinoi¹

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Section: Discussionsupporting

confidence: 73%

Section: Gap Resonant Effectsmentioning

confidence: 68%

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Analysis of wave resonant effects in-between offshore vessels arranged side-by-side

Dinoi¹

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“…O estudo da dinâmica de massa variável possui grande aplicabilidade na engenharia, em particular, na engenharia naval, como pode ser visto na Ref. [1], em que há o estudo de três sistemas que requerem análises mais sofisticadas dos efeitos da variação da massa: o moonpool, que serve para estabelecer o equilíbrio de plataformas petrolíferas em alto mar; o impacto de corpos rígidos contra a superfície daágua, que modela o impacto sofrido pela proa de navios que navegam sobre ondas; e a implantação de cabos no fundo do oceano, queé um procedimento usual em engenharia naval e offshore.…”

Section: Introductionunclassified

Máquina de Atwood com massa variável em movimento oscilatório atípico

Lucatto

Caprecci

Gonçalves

et al. 2014

Rev. Bras. Ensino Fís.

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O problema da máquina de Atwood com massa variávelé apresentado neste trabalho através de uma configuração robusta, que permite a aquisição de dados da dinâmica do movimento oscilatório durante um intervalo de tempo relativamente longo. O sistemaé facilmente implementado através da utilização de uma polia e um conjunto de três corpos cujas massas obedecem a relação M > m1 > m2 e M < m1 + m2. O problema pode ser tratado de maneira lúdica para alunos do ensino médio ou com uma profundidade maior, através da utilização do formalismo Lagrangiano, para estudantes de nível superior. O movimento oscilatório do sistema não se assemelha com nenhum dos casos de amortecimento periódico ou aperiódico observado na literatura, pois a massa do sistema varia em intervalos de tempo não constantes. Através da utilização de fotogates (sensores) acoplados a polia e do software Tracker obteve-se um conjunto de variáveis dinâmicas para comparação com os resultados esperados oriundos da descrição analítica. Palavras-chave: máquina de Atwood, dinâmica, movimento oscilatório, massa variável.An Atwood machine with variable mass is presented in this work using a robust configuration that enables data acquisition from the dynamic oscillatory motion during a relatively long time interval. The system is easily implemented through the use of a pulley and a set of three bodies whose masses satisfy the relationship M > m1 > m2, and M < m1 + m2. The problem can be treated in a playful way for high school students or with greater depth, using the Lagrangian formalism for undergraduate students. The oscillatory motion of the system is not similar to any of the cases of periodic or aperiodic damping reported in the literature, because the mass of the system changes with decreasing time intervals. Through the use of photogates (sensors) coupled to the pulley and Tracker Software it was obtained a set of dynamic variables to be compared with the expected results derived from the analytical description. Keywords: Atwood machine, dynamics, oscillatory motion, variable mass. IntroduçãoSistemas de massa variável constituem uma aplicação interessante das leis da dinâmica, e normalmente são introduzidos no curso de Física 1, a fim de exercerem o papel de uma primeira aplicação das ferramentas de cálculo adquiridas no primeiro semestre do ensino superior. Existem diversos problemas clássicos, que geralmente envolvem correntes em queda, foguetes expelindo gases ou esteiras de transporte de minério. O estudo da dinâmica de massa variável possui grande aplicabilidade na engenharia, em particular, na engenharia naval, como pode ser visto na Ref.[1], em que há o estudo de três sistemas que requerem análises mais sofisticadas dos efeitos da variação da massa: o moonpool, que serve para estabelecer o equilíbrio de plataformas petrolíferas em alto mar; o impacto de corpos rígidos contra a superfície daágua, que modela o impacto sofrido pela proa de navios que navegam sobre ondas; e a implantação de cabos no fundo do oceano, queé um procedimento usual em engenharia ...

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“…Apart from the classical rocket problem or the problem of a chain being coiled up at a table, some interesting examples of such systems can be found in the textile industry (Cveticanin (1998)) or devices in which cables are deployed or retrieved, such as tethered satellites (Crelling et al (1997)) and lifting cranes in off-shore engineering (Pesce et al (2006)). From…”

Section: Introductionmentioning

confidence: 99%

Port-Hamiltonian Modeling of Systems with Position-Dependent Mass

Jeltsema

Dòria‐Cerezo

2011

IFAC Proceedings Volumes

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It is known that straightforward application of the classical Lagrangian and Hamiltonian formalism to systems with mass varying explicitly with position may lead to discrepancies in the formulation of the equations of motion. Systems with mass varying explicitly with position often arise from situations where the partitioning of a closed system of constant mass leads to open subsystems that exchange mass among themselves. One possible solution is to introduce additional non-conservative generalized forces that account for these effects. However, it remains unclear how to systematically interconnect the Lagrangian or Hamiltonian subsystems. In this paper, systems with mass varying explicitly with position and their properties are studied in the port-Hamiltonian modeling framework. The portHamiltonian formalism combines the classical Lagrangian and Hamiltonian approach with network modeling and is applicable to various engineering domains. One of the strong aspects of the port-Hamiltonian formalism is that power-preserving interconnections between portHamiltonian subsystems results in another port-Hamiltonian system with composite energy and interconnection structure. The motion of a heavy cable being deployed from a reel by the action of gravity is used as an example.

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The Lagrange equations for systems with mass varying explicitly with position: some applications to offshore engineering

Cited by 19 publications

References 5 publications

Analysis of wave resonant effects in-between offshore vessels arranged side-by-side

Analysis of wave resonant effects in-between offshore vessels arranged side-by-side

Máquina de Atwood com massa variável em movimento oscilatório atípico

Port-Hamiltonian Modeling of Systems with Position-Dependent Mass

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